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New Results for additive and multiplicative risk apportionment

Author

Listed:
  • Henri Loubergé

    (UNIGE - Université de Genève = University of Geneva)

  • Yannick Malevergne

    (UP1 - Université Paris 1 Panthéon-Sorbonne, PRISM Sorbonne - Pôle de recherche interdisciplinaire en sciences du management - UP1 - Université Paris 1 Panthéon-Sorbonne)

  • Béatrice Rey

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

Abstract
We provide new characterizations of the preference for additive and multiplicative risk apportionment when risk ordering relies on stochastic dominance. We then point out a simple property of risk apportionment with additive risks: Quite generally, an observed preference for additive risk apportionment in a specific risk environment is preserved when the decision-maker is confronted to other risk situations, so long as the total order of stochastic dominance relationships among risk couples remains the same. The main objective of this paper is to check whether this simple property also holds for multiplicative risks environments. We explain why this is not the case in general, and then provide a set of conditions under which this property holds. We also show that it holds – and even more strongly – in the case of CRRA utility functions due to a particular feature of this family of utility functions.

Suggested Citation

  • Henri Loubergé & Yannick Malevergne & Béatrice Rey, 2020. "New Results for additive and multiplicative risk apportionment," Post-Print halshs-02930294, HAL.
    • Handle: RePEc:hal:journl:halshs-02930294
    DOI: 10.1016/j.jmateco.2020.07.004
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-02930294
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    References listed on IDEAS

    as
    1. Hongxia Wang, 2019. "Generalized Multiplicative Risk Apportionment," Risks, MDPI, vol. 7(2), pages 1-9, June.
    2. Whitmore, G A, 1970. "Third-Degree Stochastic Dominance," American Economic Review, American Economic Association, vol. 60(3), pages 457-459, June.
    3. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    4. Menezes, Carmen F. & Wang, X.Henry, 2005. "Increasing outer risk," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 875-886, November.
    5. EECKHOUDT, Louis, 2012. "Beyond risk aversion: why, how and what's next?," LIDAM Reprints CORE 2514, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Eeckhoudt, Louis & Schlesinger, Harris & Tsetlin, Ilia, 2009. "Apportioning of risks via stochastic dominance," Journal of Economic Theory, Elsevier, vol. 144(3), pages 994-1003, May.
    7. Denuit, Michel & Rey, Beatrice, 2013. "Another look at risk apportionment," LIDAM Reprints ISBA 2013027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Eeckhoudt, Louis & Schlesinger, Harris, 2008. "Changes in risk and the demand for saving," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1329-1336, October.
    9. Cary Deck & Harris Schlesinger, 2010. "Exploring Higher Order Risk Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(4), pages 1403-1420.
    10. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
    11. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    12. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, vol. 52(1), pages 146-153, January.
    13. Attema, Arthur E. & l’Haridon, Olivier & van de Kuilen, Gijs, 2019. "Measuring multivariate risk preferences in the health domain," Journal of Health Economics, Elsevier, vol. 64(C), pages 15-24.
    14. Caballe, Jordi & Pomansky, Alexey, 1996. "Mixed Risk Aversion," Journal of Economic Theory, Elsevier, vol. 71(2), pages 485-513, November.
    15. Michel Denuit & Béatrice Rey, 2013. "Another look at risk apportionment," Post-Print halshs-03353453, HAL.
    16. Gollier, Christian, 2019. "Variance stochastic orders," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 1-8.
    17. W. Chiu & Louis Eeckhoudt & Beatrice Rey, 2012. "On relative and partial risk attitudes: theory and implications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 151-167, May.
    18. Cary Deck & Harris Schlesinger, 2014. "Consistency of Higher Order Risk Preferences," Econometrica, Econometric Society, vol. 82, pages 1913-1943, September.
    19. Sebastian Ebert & Daniel Wiesen, 2011. "Testing for Prudence and Skewness Seeking," Management Science, INFORMS, vol. 57(7), pages 1334-1349, July.
    20. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    21. Y Malevergne & B Rey, 2010. "Preserving preference rankings under non-financial background risk," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1302-1308, August.
    22. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
    23. Jean, William H, 1980. "The Geometric Mean and Stochastic Dominance," Journal of Finance, American Finance Association, vol. 35(1), pages 151-158, March.
    24. Christophe Courbage & Henri Loubergé & Béatrice Rey, 2018. "On the properties of high-order non-monetary measures for risks," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 77-94, May.
    25. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    26. Denuit, Michel & Rey, Béatrice, 2013. "Another look at risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 335-343.
    27. David Crainich & Louis Eeckhoudt & Alain Trannoy, 2013. "Even (Mixed) Risk Lovers Are Prudent," American Economic Review, American Economic Association, vol. 103(4), pages 1529-1535, June.
    28. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    29. Cary Deck & Harris Schlesinger, 2018. "On The Robustness Of Higher Order Risk Preferences," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(2), pages 313-333, June.
    30. Eeckhoudt, Louis & Etner, Johanna & Schroyen, Fred, 2009. "The values of relative risk aversion and prudence: A context-free interpretation," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 1-7, July.
    31. Wang, Jianli & Li, Jingyuan, 2010. "Multiplicative risk apportionment," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 79-81, July.
    32. Louis Eeckhoudt, 2012. "Beyond Risk Aversion: Why, How and What's Next?*," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(2), pages 141-155, September.
    33. Trautmann, Stefan T. & Kuilen, Gijs van de, 2018. "Higher order risk attitudes: A review of experimental evidence," European Economic Review, Elsevier, vol. 103(C), pages 108-124.
    34. Menegatti, Mario, 2014. "New results on the relationship among risk aversion, prudence and temperance," European Journal of Operational Research, Elsevier, vol. 232(3), pages 613-617.
    35. Lajeri-Chaherli, Fatma, 2004. "Proper prudence, standard prudence and precautionary vulnerability," Economics Letters, Elsevier, vol. 82(1), pages 29-34, January.
    36. Jokung, Octave, 2011. "Risk apportionment via bivariate stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 448-452.
    37. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    38. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56(4), pages 279-279.
    39. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
    40. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "A class of bivariate stochastic orderings, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 31-50, March.
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    More about this item

    Keywords

    Additive vs. multiplicative risks; Constant relative risk aversion; Higher order risk aversion; Expected utility; Higher order risk apportionment; Stochastic dominance;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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